It was the moment everyone had been waiting for. The US president was about to take the stage and the Marine Band, laid on by the White House especially for the occasion, had begun to sound the opening notes of the traditional Hail to the Chief.

Suddenly, there was an unexpected glitch. "Can we go with the song we talked about?" Barack Obama said as he came to the podium. The band switched tack and began belting out the Bruce Springsteen classic, Born in the USA.

It was Obama's best joke of the night, delivered in the classic, self-deprecating style that has been handed down from president to president. Every president since Grover Cleveland has subjected himself to the ritual humiliations of the annual Gridiron Club dinner, hosted by Washington's political journalists, where they have come to mock and be mocked.

In Obama's case, the joke was focused on the ongoing conspiracy theory – more than half of Republican primary voters are said to believe it – that the president was not born in the US. In his speech to more than 600 journalists, officials and celebrities at a Washington hotel, Obama returned to the theme later.

As he ridiculed little-known Tim Pawlenty, the former governor of Minnesota who has his eye on running against him for president next year, Obama said: "The American people are going to have some tough questions for Tim.

"Specifically, 'Who are you and where do you come from?'" After a split second pause, he continued: "Which is OK. Two years into my presidency and I'm still getting those questions."

He had another crack at the joke in reference to the Indiana governor Mitch Daniels, who had delivered the after-dinner speech for the Republicans. He told the potential 2012 candidate: "Your friends at Fox News say you don't look like a president. Well, don't worry about it, they say the same thing about me every day."

Obama also jousted with Haley Barbour, Mississippi's chubby governor, who is yet another possible candidate in 2012 and displays the south's famous fondness for barbecue ribs and other fatty foods. Obama thanked him for supporting the first lady's anti-obesity drive, then added: "Haley, when Michelle said you should run, she didn't mean for president."